 We need sunglasses early around here. Okay, well we are going to talk about categoricals. To understand categoricals, yet to understand propositions. Propositions are what are true or false. It is early in the morning. That is true. Man, that is a sentence. That's true. There's 98 dogs behind me. That is false. Propositions are what are true or false. Not every sentence is a proposition. Not every sentence is a proposition. There are plenty of sentences that are not propositions. What time is it? That's a sentence. But that's an interrogative. It's a question. Questions are neither true nor false. Go lay down. If I'm talking to my dog, go lay down. That is an imperative, a command. That is also neither true nor false. Imperatives are either followed or not followed. Questions are either answered or not answered. Okay, but, or have an answer or don't have an answer, but propositions. Propositions are what are true or false. When we're dealing with categoricals, categoricals are propositions that compare things of one kind to things of another kind. This is where we're talking about categories. Categories of things. Consider lake. Lake is a category. It contains, in a sense, refers to all lakes. This is a lake. This is Lake Brownwood. This is not all lakes, just one. But when I say lake, I'm referring to all lakes, including this one. So when we are compared, when we have categoricals, we're comparing things of one kind to things of another kind. We're comparing the subject to the predicate. The subject is what's described by the predicate. So all lakes have water. All lakes are water bodies. Okay, so the subject there are lakes. That's the subject. The subject is lakes. The predicate is bodies of water. So here's a categorical. All lakes are bodies of water. Lakes is the subject. Bodies of water is the predicate. Now the predicate, of course, contains more than just lakes. So all lakes are bodies of water. That's true, but all bodies of water are lakes. That's false. So all lakes are bodies of water. Other bodies of water are oceans, rivers, ponds, streams, seas. These are all bodies of water. Lakes is just one of them. Okay, when we're dealing with categoricals, we have four parts. We have the subject and we have the predicate. We just talked about the subject and the predicate, right? The subject is what's described by the predicate. The predicate is what describes the subject. We also have the quantifier and the copula. So we got the subject, the predicate, the quantifier, and the copula. So we deal with categoricals. Categoricals are propositions. Propositions are either true or false. I gave an example of a categorical earlier. All lakes are bodies of water, right? And in that categorical, we have the subject and the predicate. Lakes is the subject. The predicate is bodies of water. The subject is described by the predicate. The predicate describes the subject. So I repeat myself a lot. I'm a big believer in repetition. So if you're not, I apologize in advance. All right. We have two other parts to categorical. We have the subject and the predicate. That's two parts. The other two parts are the quantifier and the copula. Now the quantifier tells us how many. How many of the subject is described by the predicate, right? So all is our quantifier. When I say all lakes are bodies of water, that's all lakes, not just some. All lakes. Every single lake is a body of water. All right. That's the quantifier. We have two other quantifiers. We have all, right? We have two other quantifiers. We have some, and we have new, right? So some lakes are in North America, right? In North America is a predicate. Lakes is the subject. Still, right? Still got the subject as lakes. Predicates now in North America. And we have the quantifier. Some. Some lakes are in South America. Some lakes are in Africa. Some lakes are in Asia, right? We can, you know, list all the continents. Well actually, sorry, not Antarctic or the Arctic. Anyway, so we have quantifiers, right? Quantifiers tell us how many. All says all of them. Some is some of them. At least some of them, I should say at least one. Maybe more. Not necessarily, but maybe more, right? And the reason why I say that, right? I had the categorical earlier. All lakes are body of water. Well that's true. What's also true are some lakes are bodies of water. Sure, that's true. Now it sounds funny to your ears because you're like, but, but, but it's all lakes are bodies of water. Well yes, all lakes are bodies of water, but if all lakes are bodies of water then at least some are. Okay, remember it's just true or false. That's all we're worried about here. We're not worried about what isn't said. Only what is said, right? Okay, so we got all lakes of bodies of water, all the quantifiers. Some, some lakes are in North America. Some is the quantifier. Then we have no, right? We have another quantifier. No. All tells us every member of the subject is described by the predicate. Some tells us at least some of the members of the subject are described by the predicate. No tells us that no members of the subject are described by the predicate. So no lake is what? No lake is composed of gravel. Or no lake is made of cookies. No lake, I wish I could say no lakes are on fire, but some lakes have actually caught fire because of all the pollution that's in them. No lake is gaseous, right? No lake is just a gas. I mean there's gasses in there chemically speaking, but no lake is, you know, in a gaseous state. It's in a liquid state. No lake is a member of Congress. I mean these are kind of ridiculous. Sorry about that, but no lake is a living thing. How about that? No lake is a living thing. Lakes aren't alive, right? Lakes aren't alive. They have living things in them, right? They are necessary for living things. Okay, but they themselves are not alive, much like the air, right? The atmosphere. The atmosphere is not alive. Okay. Or no lake can perform algebra. No lake is human. How about that? No lake is human. Let's do that, right? No lake is an animal. Maybe you want to say lakes are alive. Okay, fine. Have at it. Have fun. But at the very least, no lake is an animal, right? No lakes are animals, right? The subject is lakes, predicate animals. And when we say no lake, animals, we're saying that every member of lake, right, is not described by an animal. Now, maybe we, we could also phrase that one, right, in a particular way, but we're going to get to, you know, just a kind of forecast, right? We say no lakes are animals. We could also say our lake, all lakes are not animals, right? I don't want to confuse it too early, but just keep in mind, right, we got all, some, and no. Those are three quantifiers. We're talking about categoricals. Categoricals are a kind of proposition. Propositions are either true or false. A categorical has four parts. The quantifier, the subject, the predicate, and the coppola, right? The subject is what's described by the predicate. The predicate describes the subject. The quantifier tells us how many. So we have all lakes are bodies of water, all is the quantifiers, lake is the subject, bodies of water is the predicate. The copula is what tells us whether the subject is described by the predicate or not, and in this case is the word are. Now just kind of foreshadowing, right? There's a variety of different copula. They're basically the to be verbs. There's going to be some variation, but it's basically the to be verbs, right? Is, is, is, to be, is, was, to be, is, was, were, be, being, been, right? Those are the to be verbs. I can't believe I stumbled on that. So the copula tells us whether the subject is described by the predicate or not. All lakes are bodies of water, are is the copula, all lakes are not animals, are not is the copula. So quantifier subject predicate copula. Copula tells us whether the predicate describes the subject or not. Are or are not, is or is not. All lakes are bodies of water, are is the copula, all lakes are not mammals, are not is the copula. All right, so we have our four parts to the categorical. Quantifier subject predicate copula. Depending on your combinations of parts, you're going to have four different kinds of categoricals. Four different kinds of categoricals. Let's look at that next. Okay, so the first kind of categorical we're going to deal with is called universal affirmative. Remember our four parts to a categorical quantifier subject predicate copula. What a universal affirmative does is it tells us that every member of the subject is described by the predicate. So we already had some examples. All lakes are bodies of water, all lakes are bodies of water. Every single one. There is no lake that is not a body of water, right? So all lakes are bodies of water. That's a universal affirmative. Every member of the subject is described by the predicate. All dogs are mammals. Quantifier all, subject dog, copula are predicate mammal. All mammals are warm-blooded. All right. Again, all for the universe, all for the quantifier, mammal for the subject, or for the copula, warm-blooded for the predicate. All mammals are animals. Also a universal affirmative. So this is our first kind of categorical universal affirmative. It says every member of the subject is described by the predicate. Every single one. None left out, right? All right. That's our first kind. Let's try the next one. So the first kind of categorical we had was universal affirmative. It's universal in the sense that every member of the subject is involved. It's affirmative in the sense that every member of the subject is described by the predicate, right? Is described by the predicate. The affirmative is described by the predicate. Okay. That's what makes a universal affirmative. Let's look at universal negative. Let me, I'll let you take a stab at what this means, right? Universal, we just got finished saying this. Every member of the subject is involved. It's negative in the sense that it's not described by the predicate. It's not described by the predicate, right? Universal negative. All lakes are not animals, right? All lakes are not animals. So universal sense that it's dealing not just with this lake, but with every single one is not described by the predicate animal, right? All animals are not plants. All animals are not plants, right? All what? All stars are not animals. Celestial bodies up in the sky, stars, every single one is not an animal, right? Let's think of another one. All plants are not animals. So we have the, you have the quantifier all, subject, say we'll go back to lakes, lake, predicate, copula are not predicate animal. Okay. Now that's one formulation for the universal universal negative. This is an important lesson to remember. The words in particular are not what's going to make a categorical one of the particular kinds. You have to comprehend the meaning. So I said all lakes are not animals. That's true, right? We have a quantifier all and a copula are not. Well we could also say no lakes are animals. That is still a universal negative. Different quantifier instead of all, now we have no, different copula, all right, instead of are not we have are, right? We could even, you know, I was dealing with the the plural with lakes and animals. We can deal with the singular, no lake is an animal, right? Now it's a different, still a different copula because now we have is, right? So what makes a categorical categorical is not necessarily the word, right? So not every universal affirmative, excuse me, not every categorical beginning with the quantifier all is a universal affirmative, right? Okay, what it is going to be, what the proposition means, right? What the proposition means. Universal affirmative, every subject is described by the predicate, universal negative, every subject is not described by the predicate. So all lakes are bodies of water, universal affirmative. No lake is an animal, no lakes are animals, all lakes are not animals, all three of those are universal negatives, universal negatives, right? Saying the subject is, every member of the subject is not described by the predicate. Quick review time, quantifier, how many are involved, copula, whether the subject is described by the predicate or not, subject is what described by the predicate, predicate is what describes the subject, right, or what describes universal affirmative, every member of the subject is described by the predicate, universal negative, every member of the subject is not described by the predicate. These are all propositions, propositions are what are true or false. Two more to go. Are the universal affirmative and the universal negative are categoricals that deal with every member of the subject, universal affirmative says every member of the subject is described by the predicate, the universal negative says every member of the subject is not described by the the predicate. The particular categoricals deal with at least one, at least one. Alright, so some lakes are in North America. The quantifier there is some, the copula you're familiar with already is are, subject is lake, in North America is a predicate. Alright, some lakes are in North America. That says that at least one of the lakes, in this case it was true, right, at least one of the lakes is in North America. There are many in North America. Some lakes are in Minnesota. A lot of lakes are in Minnesota. But the particular affirmative says at least some members of the subject are affirmed, are described by the predicate. That's particular affirmative, particular because it's only dealing with some members of the subject. Alright, the other kind of particular is particular negative. Some lakes are in North America. By the way, some lakes are not in North America. Just because some lakes are in North America, that doesn't mean that some aren't. So particular negative says that at least some members of the subject are not described by the predicate. At least some lakes are in North America. Some lakes are in North America. Some lakes are not in North America. Alright, some mammals are dogs. Some mammals are not dogs. These are both true. Some mammals are dogs. That's a particular affirmative. Some mammals are not dogs. That's the particular negative. Some pets are cats. Alright, some pets are cats. I feel bad for cat owners, but hey, getting sorry, sorry, sorry. Some pets are cats. That's a particular affirmative. Some pets are not cats. That's a particular negative. Some what? Some students attend San Antonio College. Some students are not at San Antonio College. A particular affirmative, particular negative. So we've got four kinds of categoricals. Universal affirmative, universal negative, particular affirmative, particular negative, universal affirmative says every member of the subject is described by the predicate. Universal negative says every member of the subject is not described by the predicate. Particular affirmative says at least some members of the subject are described by the predicate. Particular negative, at least some members are not described by the predicate. Not necessarily all, by the way. Don't jump ahead of yourself, but not necessarily all. If a particular affirmative means that, okay, all of them are, then there's no difference between particular universal, but clearly there is. All right, anyway. Doesn't rule it out either, but let's leave that aside, right? We'll get to that couple chapters from now. So we got the four kinds of categoricals, universal affirmative, universal negative, particular affirmative, particular negative. All categoricals are composed of four parts. You have the quantifier, which tells you how many of the subjects are either described or not described. You have the subject, which is described by the predicate. You have the copula, which is whether it is described or not. And the predicate, which is what does the describing, right? Does the describing. Okay, that's four kinds of categoricals, four kinds of categoricals. And you'll be expected to identify not only which of the four kinds that you're dealing with, but identify the parts, identify the parts. Okay. And, you know, particular, right, you know, what you really need to be able to identify is universal versus particular, affirmative versus negative. Universal versus particular, affirmative versus negative. All right, I just got finished saying in the last video that categoricals have four parts, every categorical has four parts, quantifier, subject, copula, predicate. Now, I did warn you that the particular words used, you know, that doesn't necessitate what kind of categoricals involved. Because, you know, while, you know, want to try to, you know, deal with categoricals, very few sentences are sound like, you know, all lakes are bodies of water, right? A lot of times you just get lakes or bodies of water. That's fine, right? I'm not knocking this is this is what happens with a natural language like English, right? The more we get into logic, we're going to have a, you know, artificial language or formal language, right, using a lot of symbols and as, you know, removing as much ambiguity as possible. English, all natural languages are not like, especially English, right? English loves to make a whole bunch of rules and then break them. So for instance, right, all lakes are bodies of water, right, we try to have our nice parts of our categoricals there. Well, a lot of times in English, you're going to have some lakes are not, I'm sorry, you're going to have, you're just going to have lakes are bodies of water, right? Or this lake is beautiful. Or, right, lakes are cool. Okay, that's fine, right? But you have to be able to identify the parts, you have to be able to translate, right, these, these sentences and plain natural English into our categoricals. Now, unfortunately, since, like I said, English loves to make up, have a bunch of rules and then break them. There are no hard and fast rules for doing this translation. You're going to have to rely upon the context. You're going to have to rely upon the meaning of the sentence within that context in order to translate it. So what, you know, the, the difference is, right, what you have to look out for is our four kinds of categoricals, whether every member of the subject is identified, is described by the predicate, that's universal formative, every member of the subject is not as universal negative, particular formative, at least one member, right? And particular, a particular formative and particular negative, at least one member of the subject is not. Let's go through a few examples and some noticeable cases. Alright, so I guess I've finished saying that English isn't always some neat and tidy when it comes to its quantifier subjects, copy those predicates. This is true. So one case, for example, is a categoricals of singulars, right? And this is, you know, these are categoricals with one and only one subject. There's only one and only one thing in the subject class. So this works, we're dealing with like individuals. So Dr. Hogan is shooting a video. Okay. Dr. Hogan shoots video. Dr. Hogan teaches philosophy. These are propositions, and they are understood as categoricals. Lake Brownwood is in Texas. That's a singular. There's one and only one thing that is Lake Brownwood. Now, here's the question. When you have a subject class of one and only one thing, what kind of categorical is it? Remember we got universal formative, universal negative, particular formative, particular negative, right? Now, whether you're dealing with a singular, that doesn't affect whether it's affirmative or negative, right? Because you could say Dr. Hogan is shooting a video. You can also say Dr. Hogan is walking on the moon. The first is an affirmative. The first, sorry, Dr. Hogan is not walking on the moon. The first is an affirmative. The second is the negative. It doesn't matter whether you're dealing with a singular or not, right? That's not a... What is important here is whether you've got a universal or a particular. So what do you think? Dr. Hogan is shooting video. Is that a universal affirmative or is that a particular affirmative? Now, you might think, well, it's a particular affirmative because you got only one. Okay. Now, remember, the particular says at least one member of the subject class. Okay, that's true, right? I mean, there's at least one member of the subject class of shooting video. That's Dr. Hogan. But the universal affirmative says every member of the subject class is described by the predicate. How many members, we would say Dr. Hogan is shooting video. How many members are shooting? One. How many are out there? One. So how many? All of them. Now, that sounds a little funny to your ears, but every member of the subject class, namely me, is shooting video. Therefore, Dr. Hogan is shooting video is a universal affirmative. Universal affirmative. Dr. Hogan is not walking on the moon. That's a universal negative. When we say every member of the subject class, we're not saying just some, right? We're saying every member of the subject class. Therefore, this, you know, when we deal with the categoricals of singulars, it's going to be a universal. It's going to be universal. Whether it's a universal affirmative or universal negative. So let's talk about English grammar a second. In English grammar, there's a part of speech called the article. Article is not what not in this sense, not what you know that thing that you had to read for your courses. That's not what I'm talking about. An article is a word and part of speech, right, that's used to mitigate quantity. Now immediately, this should get you thinking of quantifiers. And that's right, right, deals with quantifiers. Unfortunately, there's no hard and fast rules with the article to tell us whether we're dealing with the universal or the particular. Oops, that's frustrating. All right. So there's two kinds of articles, you know, at least to start, we're going to deal with two kinds of articles, the definite and the indefinite. The definite uses the word the. Right. The lake is cool. Right. That's the word the, that's the definite article. The indefinite uses the word is either a or n. Right. A bird is flying. Right. That's the indefinite article. Now the points to a specific one. Now immediately, usually it points to a specific one. Now immediately, this might get you to think that we'll deal with a particular there. Right. The lake is cool. All right. At least one lake is cool. Okay. Maybe, right, but as far as, you know, that's concerned, we could also say the lake is a body of water. The bird is a mammal. I'm sorry, the bird is an avid. The bird is an animal. Depending on context, that can either be the particular or the universal. Right. So there's no, there's no hard and fast rules when you're dealing with a definite article to determine whether you're dealing with the universal or a particular. You have to rely upon context, you have to rely upon the meanings of the terms. And in some cases you have to rely upon, you know, which one's actually going to be true. Right. So the lake is cool. All right. Or, you know, that, that's fine. Is every lake cool? Not really. I mean, some get pretty warm. So I'm a dime refrigerant. Right. Or the lake is calm. Okay. That's probably a particular. Because not every lake is calm. So you have to rely upon context or rely upon which one's going to be true. Okay. That's the definite article. The indefinite article is pretty much the same way. Right. They can either be used for the particular or the universal depending upon context, depending upon the meaning. And in some case, which one's going to be true. Right. So a boat is on the water. That's true. Right. That doesn't mean every boat is on the water. Right. Lots of boats are in dry dock. Lots of boats haven't been sold yet. Lots of boats are sitting in driveways. So a boat is on the water. That's not true as the universal. It's true as a particular. It's true as a particular a lake is a body of water. Well, yeah, that's true as universal. Right. There are no lakes or not bodies of water. Right. Okay. So, you know, as a matter of fact, the indefinite article doesn't determine necessarily whether you're dealing with the universal or a particular. You have to look to context. You have to look at the understanding meaning of the terms. And again, in some cases, you just have to rely upon what's true. Right. You're not to figure out, okay, was this going to be true as a universal true as a particular I mean, it can be both in some cases. Right. Not every case can be both in some cases. And again, sorry, English has lots of rules and we'd like to break them. So there's no determined way to figure that you're going to have to comprehend what's going on. All right. So let's take a look at the proper article and the absent article. The proper article looks a lot like the definite article because it uses the same word. English got to love it. So the proper article is used to indicate like a singular thing. Almost like a name. So the White House, the Pacific, the winner of the race. So the proper article gives us one and only one thing is what is happening with the proper article. And as far as chemical articles are concerned, yeah, they work just the same way as the Singulars. Right. Remember we dealt with Singular earlier? Well, when we're dealing with the proper article, they're treated as universals because it's the one and the only one. Now, the proper article is used most on what we're dealing with like a name or something kind of famous. Right. Even if a couple of generic terms are used for, so the White, that's a generic term, House, that's a generic term, but the White House. Right. Now you got a name for something in particular. Okay. So that's the proper article. The proper article gives us one and only one thing. It's like the singular categoricals, like the categoricals of Singulars and is treated as a universal because it's dealing with every member of the subject because it's just one. The absent article is when there's no article to be found whatsoever. Lakes are bodies of water. There's no article there. It's absent. It's gone. It's mysterious. Lakes are bodies of water. Yeah. Right. That when we're dealing with the absent article, we're dealing with the kind of the implicit presumption is that it's all of them. All of them. If you don't have an article and you're dealing with like maybe just one thing, bird flies. Yeah. That sounds, that's even, that's even too harmful for, you know, even for English, right? That sounds too weird, even for English. So when we're dealing with the absent article, the implicit presumption that it's, it's, it's universal. And it, you know, where the proper article is dealing with just one, the absent article looks like it's dealing with all of them. Right. Um, if, you know, if I start speaking about myself in the third person, right, with an article, Dr. Haugen is shooting video right now. It's like, okay, what's wrong with you? I was like, Oh, no, that, that, that sounds weird. So the proper article and the absent article are both treated as universal categoricals. Right. The proper article is because it's a categorical singular and the absent article because we're dealing with all of them. All right. So we have categorical singular, the definite, the indefinite, the proper article, the absent article. All right. I'm done dealing with articles. Let's move on to some weird things that happen with copula. We deal with the articles. Now we're going to deal with the copula. Now the cop up to this point, primarily when I deal with copula, we'll be dealing with the to-be words, is, at, is as it was, was, was, were, be, being, being. Right. Okay. But there are, I mean, English, again, I keep beating up on English. I like English don't get me wrong, but sometimes it can be frustrating. Um, there are other words that can be used as copula, frequently in English that, you know, indicate that the subject is, you know, described by the predicate. So birds have wings. All right, birds have wings. That describes birds, right? But the copula there is now have. You know, possessive verbs have, has, have been. These also can also be used as copula. You know, the to-do verbs, right? The to-do verbs, did, do, done, right? These are also used as copula, right? So Jack did the half mile, right? Okay, well, you know, that, that means that Jack ran the half mile, right? Jack is amongst the people that ran the half mile. Okay, I did the dishes, right? The did, you know, the to-do verb there, did the verb, did the dishes. That is the copula there. Even, you know, got, right? I got sweaty, right? That's, you know, version of the, you know, the possessive verb. But, you know, that, that's still, the predicate still describes the subject. So sometimes the copula verb is going to be, you know, non-standard. It's not going to be the to-be verb. It's actually a long list of these things. Too many, then I'm gonna, I'm not gonna try and go on too long. If you're curious, look them up. And, you know, earlier we talked about absent articles. Well, sometimes the copula is absent, too, right? Sometimes the copula is absent, too. The lake flows, rather sorry, the river flows, right? The river flows. Okay, well, that's a subject. It's actually also, so we got the definite article, right? We have the subject, the rivers. No copula, but the predicate flows or flowing, right? That tells us that, that, at least that river is amongst the things that flow. Now, here's an interesting question. Is the river flows, is that a universal or a particular? I mean, it could be understood out of the way, right? Where the river talk about all rivers, or the river, that river that we're talking about. Yeah, so that's an interesting sort of question. Whether the river flows is going to be universal or particular. And again, you know, say this again, that depends upon context. So I have to probably look at that one sentence amongst all the sentences in that paragraph or whatever you're reading, right? All right. So we have the non-standard copula, and you have the absent copula. Now, whether it's non-standard or not, that's not going to determine whether it's an affirmative or negative. Probably, I'm going to hazard a guess here, but I haven't thought about this, so, you know, I might need a backtrack later on. But I'm going to guess if the copula is absent, it's always an affirmative. But, yeah, let's put a thumbtack on that, right? Or maybe, you know, maybe the idea is, if you have no clue, right? Guess affirmative. But, you know, what the copula does is tells us whether the predicate describes it or not. So you have to look into context, you have to look at the meanings of the sentence to determine whether the predicate describes the subject or not. That's going to determine whether it's an affirmative or negative, right? So, yeah, English is fun. We got all these rules and we love to break them. We have these categoricals, and what you have to do, what you're expected to do, is to be able to identify which of the four kind of categoricals you have and the parts of those, the parts of the categorical. The quantifier, the subject, the predicate, the copula, right? So, here's birds fly. Well, now the quantifier is absent and the copula. So, is it a universal of particulars, an affirmative or a negative? Fish swim. Animals breathe. Sun shines. Quantifier's absent. Copula's absent. You still have to identify which kind of categorical it has. You know, if we, if the parts are missing, well, okay, then the parts are missing. And you just kind of note that. But the, but what's important to remember here is anyway, we got four kinds, universal, affirmative, universal, negative, particular, affirmative, particular, negative, what makes a universal particular, whether we're dealing with all members of the subject or just, or just some, or at least, I'm sorry, not just, at least some, right? At least one, affirmative or negative, whether the predicate describes or is not, just does not describe. All right. Those are our four kinds of categoricals. Believe it or not, this is just getting started. This is the really easy stuff, getting started with logic. When we have to think about nexus, well, then what can we do with these? What inferences can we make?